What is the difference between Amitābha's Sukhāvatī & the Lotus Vault?

What is the relation of sukhāvatī to 蓮華藏莊嚴世界海 ("the lotus's vault, the perfected lokadhātu, the ocean") attested to in the Buddhāvataṃsakanāmamahāyānasūtra T279 & Āryasaddharmapuṇḍarīkanāmamahāyānasūtra T262, wherein arahantaḥ, according to the Mahāyāna as attested to in aforementioned scriptures, perfect Buddhahood? Context: > Inquiry: in the Arhat's past lives the causes and conditions for being > subject to embodiment necessarily ought to have been eradicated, in > light of this they dwell where to perfect buddhahood? > > Response: when attaining arhatship, the three realms' myriad outflows' > causes and conditions are exhausted, there is no more birth again in > the three realms. There is a pure buddha land, beyond the three > realms, where not even the word affliction has a name, in this kingdom > of the Buddha, they hear the Dharma Flower Sūtra [i.e. the Lotus > Sūtra], with this they perfect Buddhahood. As in the Dharma Flower > Sūtra's words: "There are arhantaḥ, for example, who’ve not heard the > Dharma Flower Sūtra,themselves they call 'ones who have attained > cessation'; I in another realm for them speak this matter, that you > all shall become samyaksaṁbuddhāḥ." > > (Mahāprajñāpāramitopadeśaḥ T1509.714a9) Furthermore, these pure lands, what relation do they have to ākaniṣṭaghanavyūha?